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  "body": "\n## Summary\n\nAn irreducible analytic germ is a nonempty [[germ of an analytic set|Q9B74BYZ8C]] that is not the union of two strictly smaller analytic germs.\nEquivalently, its ideal in the ring of holomorphic germs is a prime ideal.\nSince this ring is Noetherian, every analytic germ is a finite union of irreducible germs.\nThe irreducible germs are the building blocks of local analytic geometry.\n\n## Explanations\n\n### L1 human\n\nNear a point, an analytic set may consist of several pieces that only meet at the point, like two lines crossing.\nAn irreducible germ is one that cannot be split in this way.\nThe cusp $\\set{z_1^2 = z_2^3}$ is irreducible at the origin, although it is singular there.\nThe node $\\set{z_2^2 = z_1^2(1 + z_1)}$ is irreducible as a global curve, but its germ at the origin is the union of two smooth branches, so it is reducible there.\n",
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